Complex Twinning, Polytypism and Disorder Phenomena in the Crystal Structures of Antimonpearceite and Arsenpolybasite

321 The Canadian Mineralogist Vol. 45, pp. 321-333 (2007) COMPLEX TWINNING, POLYTYPISM AND DISORDER PHENOMENA IN THE CRYSTAL STRUCTURES OF ANTIMONPEARCEITE AND ARSENPOLYBASITE Luca BINDI§ Museo di Storia Naturale, Sezione di Mineralogia, Università degli Studi di Firenze, via La Pira 4, I–50121 Firenze, Italy Michel EVAIN Laboratoire de Chimie des Solides, I.M.N., UMR C6502 CNRS – Université de Nantes, 2, rue de la Houssinière, BP 32229, F–44322 Nantes Cedex 3, France Silvio MENCHETTI Dipartimento di Scienze della Terra, Università degli Studi di Firenze, via La Pira 4, I–50121 Firenze, Italy Abstract The crystal structures of antimonpearceite, arsenpolybasite-222 and arsenpolybasite-221 have been solved and refi ned from single-crystal X-ray-diffraction datasets. Antimonpearceite crystallizes in the trigonal space-group P¯3m1, with a 7.4805(5), c 11.8836(13) Å, V 575.89(8) Å3 and Z = 1. The refi nement of the structure leads to R = 0.0352 for 1095 independent observed refl ections [I/␴(I) ≥ 2] and 98 parameters. Arsenpolybasite-222 crystallizes in the monoclinic space-group C2/c, with a 26.036(2), b 15.0319(13), c 24.042(3) Å, ␤ 90.000(13)° (pseudohexagonal cell with the a = √3b orthohexagonal relation), V 9409.5(15) Å3 and Z = 16. A second-degree twinning by metric merohedry gives rise to an apparent trigonal symmetry, with the unit-cell parameters (hexagonal cell) a 15.0319(13) and c 24.042(3) Å. The refi nement of the structure leads to R = 0.0716 for 22008 independent observed refl ections [I/␴(I) ≥ 2] and 552 parameters. Arsenpolybasite-221 crystallizes in the space group P321, with a 14.9746(17), c 11.9982(6) Å, V 2330.0(4) Å3 and Z = 4. The refi nement of the structure, including a mirror-twin operation (fi rst- degree twin, ¯3'2/m'1 polychromatic point-group), leads to R = 0.0434 for 4639 independent observed refl ections [I/␴(I) ≥ 2] and 2– 2+ 184 parameters. All the structures consist of the stacking of [(Ag,Cu)6(As,Sb)2S7] and [Ag9CuS4] module layers along [001]; (As,Sb) forms isolated (As,Sb)S3 pyramids typically occurring in sulfosalts, copper links two sulfur atoms in a linear coordination, and silver occupies sites with coordination ranging from quasilinear to almost tetrahedral. The substitution of Cu for Ag in 2– the [(Ag,Cu)6(As,Sb)2S7] module layer becomes greater in going from the 111 structure, through the 221, to the 222 structure. The determination of the crystal structure for all the members of the group leads us to consider them as a family of polytypes. Keywords: antimonpearceite, arsenpolybasite, polytypism, disorder, twinning, crystal-structure determination. Sommaire Nous avons résolu et affi né la structure cristalline de l’antimonpearceïte, l’arsenpolybasite-222 et l’arsenpolybasite-221 à partir de données en diffraction X prélevées sur monocristaux. L’antimonpearceïte cristallise dans le groupe spatial P¯3m1, système trigonal, avec a 7.4805(5), c 11.8836(13) Å, V 575.89(8) Å3 et Z = 1. L’affi nement de la structure a mené à un R égal à 0.0352 pour 1095 réfl exions indépendantes observées [I/␴(I) ≥ 2] et 98 paramètres. L’arsenpolybasite-222 cristallise dans le groupe spatial C2/c, système monoclinique, avec a 26.036(2), b 15.0319(13), c 24.042(3) Å, ␤ 90.000(13)° (maille pseudohex- agonale avec la relation orthohexagonale ayant la relation a = √3b), V 9409.5(15) Å3 et Z = 16. Une macle de second degré par méroédrie métrique produit une symétrie trigonale apparente, avec les paramètres réticulaires (maille hexagonale) a 15.0319(13) et c 24.042(3) Å. L’affi nement de la structure a mené à un R égal à 0.0716 pour 22008 réfl exions indépendantes observées [I/␴(I) ≥ 2] et 552 paramètres. L’arsenpolybasite-221 cristallise dans le groupe spatial P321, avec a 14.9746(17), c 11.9982(6) Å, V 2330.0(4) Å3 et Z = 4. L’affi nement de la structure, qui comprend une opération de macle mirroir (macle de premier degré, groupe ponctuel polychromatique ¯3'2/m'1), a mené à un R égal à 0.0434 pour 4639 réfl exions indépendantes observées [I/␴(I) 2– 2+ ≥ 2] et 184 paramètres. Ces trois structures sont faites d’un empilement de modules [(Ag,Cu)6(As,Sb)2S7] et [Ag9CuS4] en couches le long de [001]; le (As,Sb) forme des pyramides (As,Sb)S3 isolées typiques des sulfosels, avec le cuivre lié à deux atomes de soufre en coordinence linéaire, et les atomes d’argent en coordinence quasiment linéaire à tétraédrique. Avec une 2– substitution du Cu pour Ag, le volume du module en couche [(Ag,Cu)6(As,Sb)2S7] augmente de la structure 111 à la structure 221, et enfi n à la structure 222. La détermination de la structure des trois membres du groupe nous pousse à les considérer une famille de polytypes. Mots-clés: antimonpearceïte, arsenpolybasite, polytypisme, désordre, macles, détermination de la structure. § E-mail address: [email protected]fi .it 322 the canadian mineralogist Introduction Background Information The minerals belonging to the pearceite–polybasite A summary of all known cell metrics and space group were divided by Frondel (1963) into two series: groups in the pearceite–polybasite group is given in the fi rst one, involving pearceite [(Ag,Cu)16(As,Sb)2S11] Table 1. To describe the complex electron-density and antimonpearceite [(Ag,Cu)16(Sb,As)2S11], is associated with Ag,Cu observed in these structures, characterized by a “small” unit-cell [labeled 111] Bindi et al. (2006a) and Evain et al. (2006a, b) used and a high Cu content; the second one, with poly- a non-harmonic model based upon a development of basite [(Ag,Cu)16(Sb,As)2S11] and arsenpolybasite the atomic displacement factor (Kuhs & Heger 1979, [(Ag,Cu)16(As,Sb)2S11], has doubled unit-cell param- Boucher et al. 1993, Evain et al. 1998). In general, in eters [labeled 222] and a low Cu content. Moreover, the the presence of atomic disorder, a split-atom approach existence of an intermediate type of unit cell, labeled is classically used in structure determinations. However, 221, was claimed for both polybasite (Harris et al. 1965, that approach has several disadvantages, and gives rise Edenharter et al. 1971) and arsenpolybasite (Minčeva- to ambiguities. As Bachmann & Schulz (1984) have Stefanova et al. 1979). From the crystallographic point demonstrated, the introduction of extra positions in the of view, these minerals were initially reported as being refi nement does not necessarily means that those posi- monoclinic C2/m, although dimensionally pseudo- tions correspond to occupied equilibrium sites. This is hexagonal (Peacock & Berry 1947, Frondel 1963, Harris particularly true in the case of fast ionic conductors, for et al. 1965, Hall 1967, Sugaki et al. 1983). Recently, which there exists a delocalization of an ionic species Bindi et al. (2006a) solved and refined the crystal over a liquid-like structure, and also where cations such structure of pearceite in the space group P¯3m1. They as a d10 element easily adopt a complicated coordination showed that the structure of pearceite can be described because of s,d orbital mixing or polarization factors as a regular alternation of two kinds of layer stacked (Gaudin et al. 2001). In addition to the problem of the along the c axis: a fi rst layer (labeled A), of general physical meaning of the refi ned positions, one usually 2– composition [(Ag,Cu)6(As,Sb)2S7] , and a second layer observes that the closer the refi ned positions in a disor- 2+ (labeled B), with a general composition [Ag9CuS4] . dered structure, the higher the correlations and the more The complex polytypism phenomena (i.e., 221 and unstable the refi nements. The use of tensor elements of 222 unit-cell types) occurring in various samples of higher order in the expression of the structure factors polybasite were studied by Evain et al. (2006a). These (the “non-harmonic approach”) is then an alternative authors solved and refi ned the crystal structure of both solution, giving an equivalent description (Kuhs 1992). polybasite-221 (space group P321) and polybasite-222 The benefi t of the latter description over the split-atom (space group C2/c), and proposed a possible mechanism model is an easier convergence of the refi nement as a regulating the stabilization of unit-cell type in these result of much lower correlations among the refi ned minerals. Finally, by means of a study of a crystal of parameters, as proven in many structure determinations Se-rich antimonpearceite (with 2.55 atoms per formula (see for instance the case of argyrodite: Boucher et al. unit Se), Evain et al. (2006b) investigated the structural 1993). In both cases, however, the refi ned coordinates role of selenium in these minerals. do not have a simple physical meaning, because they In this paper, we report the structural characteriza- are simply the fi rst-order terms in the expansion of the tion of the remaining members of the pearceite–poly- conventional structure-factor. Therefore, one must be basite group, antimonpearceite, arsenpolybasite-222 very cautious in interpreting bond distances from such and arsenpolybasite-221. refi nements. A better way to interpret the refi ned parameters is by using the joint probability-density function the crystal structures of antimonpearceite and arsenpolybasite 323 (jpdf), which can be directly calculated from the refi ned As and Se, ±0.01 for Fe, Zn, Te, Au, Pb and Bi. The parameters. This function is the weighted superposition standards employed were: native elements for Cu, Ag, of the Fourier transform of the non-harmonic atom- Au, and Te, galena for Pb, pyrite for Fe and S, synthetic displacement factors of atoms over several sites.

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